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| 132 | .rm #[ #] #H #V #F C |
| 133 | .\" ======================================================================== |
| 134 | .\" |
| 135 | .IX Title "bn_internal 3" |
| 136 | .TH bn_internal 3 "2015-07-09" "1.0.1p" "OpenSSL" |
| 137 | .\" For nroff, turn off justification. Always turn off hyphenation; it makes |
| 138 | .\" way too many mistakes in technical documents. |
| 139 | .if n .ad l |
| 140 | .nh |
| 141 | .SH "NAME" |
| 142 | bn_mul_words, bn_mul_add_words, bn_sqr_words, bn_div_words, |
| 143 | bn_add_words, bn_sub_words, bn_mul_comba4, bn_mul_comba8, |
| 144 | bn_sqr_comba4, bn_sqr_comba8, bn_cmp_words, bn_mul_normal, |
| 145 | bn_mul_low_normal, bn_mul_recursive, bn_mul_part_recursive, |
| 146 | bn_mul_low_recursive, bn_mul_high, bn_sqr_normal, bn_sqr_recursive, |
| 147 | bn_expand, bn_wexpand, bn_expand2, bn_fix_top, bn_check_top, |
| 148 | bn_print, bn_dump, bn_set_max, bn_set_high, bn_set_low \- BIGNUM |
| 149 | library internal functions |
| 150 | .SH "SYNOPSIS" |
| 151 | .IX Header "SYNOPSIS" |
| 152 | .Vb 1 |
| 153 | \& #include <openssl/bn.h> |
| 154 | \& |
| 155 | \& BN_ULONG bn_mul_words(BN_ULONG *rp, BN_ULONG *ap, int num, BN_ULONG w); |
| 156 | \& BN_ULONG bn_mul_add_words(BN_ULONG *rp, BN_ULONG *ap, int num, |
| 157 | \& BN_ULONG w); |
| 158 | \& void bn_sqr_words(BN_ULONG *rp, BN_ULONG *ap, int num); |
| 159 | \& BN_ULONG bn_div_words(BN_ULONG h, BN_ULONG l, BN_ULONG d); |
| 160 | \& BN_ULONG bn_add_words(BN_ULONG *rp, BN_ULONG *ap, BN_ULONG *bp, |
| 161 | \& int num); |
| 162 | \& BN_ULONG bn_sub_words(BN_ULONG *rp, BN_ULONG *ap, BN_ULONG *bp, |
| 163 | \& int num); |
| 164 | \& |
| 165 | \& void bn_mul_comba4(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b); |
| 166 | \& void bn_mul_comba8(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b); |
| 167 | \& void bn_sqr_comba4(BN_ULONG *r, BN_ULONG *a); |
| 168 | \& void bn_sqr_comba8(BN_ULONG *r, BN_ULONG *a); |
| 169 | \& |
| 170 | \& int bn_cmp_words(BN_ULONG *a, BN_ULONG *b, int n); |
| 171 | \& |
| 172 | \& void bn_mul_normal(BN_ULONG *r, BN_ULONG *a, int na, BN_ULONG *b, |
| 173 | \& int nb); |
| 174 | \& void bn_mul_low_normal(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n); |
| 175 | \& void bn_mul_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n2, |
| 176 | \& int dna,int dnb,BN_ULONG *tmp); |
| 177 | \& void bn_mul_part_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, |
| 178 | \& int n, int tna,int tnb, BN_ULONG *tmp); |
| 179 | \& void bn_mul_low_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, |
| 180 | \& int n2, BN_ULONG *tmp); |
| 181 | \& void bn_mul_high(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, BN_ULONG *l, |
| 182 | \& int n2, BN_ULONG *tmp); |
| 183 | \& |
| 184 | \& void bn_sqr_normal(BN_ULONG *r, BN_ULONG *a, int n, BN_ULONG *tmp); |
| 185 | \& void bn_sqr_recursive(BN_ULONG *r, BN_ULONG *a, int n2, BN_ULONG *tmp); |
| 186 | \& |
| 187 | \& void mul(BN_ULONG r, BN_ULONG a, BN_ULONG w, BN_ULONG c); |
| 188 | \& void mul_add(BN_ULONG r, BN_ULONG a, BN_ULONG w, BN_ULONG c); |
| 189 | \& void sqr(BN_ULONG r0, BN_ULONG r1, BN_ULONG a); |
| 190 | \& |
| 191 | \& BIGNUM *bn_expand(BIGNUM *a, int bits); |
| 192 | \& BIGNUM *bn_wexpand(BIGNUM *a, int n); |
| 193 | \& BIGNUM *bn_expand2(BIGNUM *a, int n); |
| 194 | \& void bn_fix_top(BIGNUM *a); |
| 195 | \& |
| 196 | \& void bn_check_top(BIGNUM *a); |
| 197 | \& void bn_print(BIGNUM *a); |
| 198 | \& void bn_dump(BN_ULONG *d, int n); |
| 199 | \& void bn_set_max(BIGNUM *a); |
| 200 | \& void bn_set_high(BIGNUM *r, BIGNUM *a, int n); |
| 201 | \& void bn_set_low(BIGNUM *r, BIGNUM *a, int n); |
| 202 | .Ve |
| 203 | .SH "DESCRIPTION" |
| 204 | .IX Header "DESCRIPTION" |
| 205 | This page documents the internal functions used by the OpenSSL |
| 206 | \&\fB\s-1BIGNUM\s0\fR implementation. They are described here to facilitate |
| 207 | debugging and extending the library. They are \fInot\fR to be used by |
| 208 | applications. |
| 209 | .SS "The \s-1BIGNUM\s0 structure" |
| 210 | .IX Subsection "The BIGNUM structure" |
| 211 | .Vb 1 |
| 212 | \& typedef struct bignum_st BIGNUM; |
| 213 | \& |
| 214 | \& struct bignum_st |
| 215 | \& { |
| 216 | \& BN_ULONG *d; /* Pointer to an array of \*(AqBN_BITS2\*(Aq bit chunks. */ |
| 217 | \& int top; /* Index of last used d +1. */ |
| 218 | \& /* The next are internal book keeping for bn_expand. */ |
| 219 | \& int dmax; /* Size of the d array. */ |
| 220 | \& int neg; /* one if the number is negative */ |
| 221 | \& int flags; |
| 222 | \& }; |
| 223 | .Ve |
| 224 | .PP |
| 225 | The integer value is stored in \fBd\fR, a \fImalloc()\fRed array of words (\fB\s-1BN_ULONG\s0\fR), |
| 226 | least significant word first. A \fB\s-1BN_ULONG\s0\fR can be either 16, 32 or 64 bits |
| 227 | in size, depending on the 'number of bits' (\fB\s-1BITS2\s0\fR) specified in |
| 228 | \&\f(CW\*(C`openssl/bn.h\*(C'\fR. |
| 229 | .PP |
| 230 | \&\fBdmax\fR is the size of the \fBd\fR array that has been allocated. \fBtop\fR |
| 231 | is the number of words being used, so for a value of 4, bn.d[0]=4 and |
| 232 | bn.top=1. \fBneg\fR is 1 if the number is negative. When a \fB\s-1BIGNUM\s0\fR is |
| 233 | \&\fB0\fR, the \fBd\fR field can be \fB\s-1NULL\s0\fR and \fBtop\fR == \fB0\fR. |
| 234 | .PP |
| 235 | \&\fBflags\fR is a bit field of flags which are defined in \f(CW\*(C`openssl/bn.h\*(C'\fR. The |
| 236 | flags begin with \fB\s-1BN_FLG_\s0\fR. The macros BN_set_flags(b,n) and |
| 237 | BN_get_flags(b,n) exist to enable or fetch flag(s) \fBn\fR from \fB\s-1BIGNUM\s0\fR |
| 238 | structure \fBb\fR. |
| 239 | .PP |
| 240 | Various routines in this library require the use of temporary |
| 241 | \&\fB\s-1BIGNUM\s0\fR variables during their execution. Since dynamic memory |
| 242 | allocation to create \fB\s-1BIGNUM\s0\fRs is rather expensive when used in |
| 243 | conjunction with repeated subroutine calls, the \fB\s-1BN_CTX\s0\fR structure is |
| 244 | used. This structure contains \fB\s-1BN_CTX_NUM\s0\fR \fB\s-1BIGNUM\s0\fRs, see |
| 245 | \&\fIBN_CTX_start\fR\|(3). |
| 246 | .SS "Low-level arithmetic operations" |
| 247 | .IX Subsection "Low-level arithmetic operations" |
| 248 | These functions are implemented in C and for several platforms in |
| 249 | assembly language: |
| 250 | .PP |
| 251 | bn_mul_words(\fBrp\fR, \fBap\fR, \fBnum\fR, \fBw\fR) operates on the \fBnum\fR word |
| 252 | arrays \fBrp\fR and \fBap\fR. It computes \fBap\fR * \fBw\fR, places the result |
| 253 | in \fBrp\fR, and returns the high word (carry). |
| 254 | .PP |
| 255 | bn_mul_add_words(\fBrp\fR, \fBap\fR, \fBnum\fR, \fBw\fR) operates on the \fBnum\fR |
| 256 | word arrays \fBrp\fR and \fBap\fR. It computes \fBap\fR * \fBw\fR + \fBrp\fR, places |
| 257 | the result in \fBrp\fR, and returns the high word (carry). |
| 258 | .PP |
| 259 | bn_sqr_words(\fBrp\fR, \fBap\fR, \fBn\fR) operates on the \fBnum\fR word array |
| 260 | \&\fBap\fR and the 2*\fBnum\fR word array \fBap\fR. It computes \fBap\fR * \fBap\fR |
| 261 | word-wise, and places the low and high bytes of the result in \fBrp\fR. |
| 262 | .PP |
| 263 | bn_div_words(\fBh\fR, \fBl\fR, \fBd\fR) divides the two word number (\fBh\fR,\fBl\fR) |
| 264 | by \fBd\fR and returns the result. |
| 265 | .PP |
| 266 | bn_add_words(\fBrp\fR, \fBap\fR, \fBbp\fR, \fBnum\fR) operates on the \fBnum\fR word |
| 267 | arrays \fBap\fR, \fBbp\fR and \fBrp\fR. It computes \fBap\fR + \fBbp\fR, places the |
| 268 | result in \fBrp\fR, and returns the high word (carry). |
| 269 | .PP |
| 270 | bn_sub_words(\fBrp\fR, \fBap\fR, \fBbp\fR, \fBnum\fR) operates on the \fBnum\fR word |
| 271 | arrays \fBap\fR, \fBbp\fR and \fBrp\fR. It computes \fBap\fR \- \fBbp\fR, places the |
| 272 | result in \fBrp\fR, and returns the carry (1 if \fBbp\fR > \fBap\fR, 0 |
| 273 | otherwise). |
| 274 | .PP |
| 275 | bn_mul_comba4(\fBr\fR, \fBa\fR, \fBb\fR) operates on the 4 word arrays \fBa\fR and |
| 276 | \&\fBb\fR and the 8 word array \fBr\fR. It computes \fBa\fR*\fBb\fR and places the |
| 277 | result in \fBr\fR. |
| 278 | .PP |
| 279 | bn_mul_comba8(\fBr\fR, \fBa\fR, \fBb\fR) operates on the 8 word arrays \fBa\fR and |
| 280 | \&\fBb\fR and the 16 word array \fBr\fR. It computes \fBa\fR*\fBb\fR and places the |
| 281 | result in \fBr\fR. |
| 282 | .PP |
| 283 | bn_sqr_comba4(\fBr\fR, \fBa\fR, \fBb\fR) operates on the 4 word arrays \fBa\fR and |
| 284 | \&\fBb\fR and the 8 word array \fBr\fR. |
| 285 | .PP |
| 286 | bn_sqr_comba8(\fBr\fR, \fBa\fR, \fBb\fR) operates on the 8 word arrays \fBa\fR and |
| 287 | \&\fBb\fR and the 16 word array \fBr\fR. |
| 288 | .PP |
| 289 | The following functions are implemented in C: |
| 290 | .PP |
| 291 | bn_cmp_words(\fBa\fR, \fBb\fR, \fBn\fR) operates on the \fBn\fR word arrays \fBa\fR |
| 292 | and \fBb\fR. It returns 1, 0 and \-1 if \fBa\fR is greater than, equal and |
| 293 | less than \fBb\fR. |
| 294 | .PP |
| 295 | bn_mul_normal(\fBr\fR, \fBa\fR, \fBna\fR, \fBb\fR, \fBnb\fR) operates on the \fBna\fR |
| 296 | word array \fBa\fR, the \fBnb\fR word array \fBb\fR and the \fBna\fR+\fBnb\fR word |
| 297 | array \fBr\fR. It computes \fBa\fR*\fBb\fR and places the result in \fBr\fR. |
| 298 | .PP |
| 299 | bn_mul_low_normal(\fBr\fR, \fBa\fR, \fBb\fR, \fBn\fR) operates on the \fBn\fR word |
| 300 | arrays \fBr\fR, \fBa\fR and \fBb\fR. It computes the \fBn\fR low words of |
| 301 | \&\fBa\fR*\fBb\fR and places the result in \fBr\fR. |
| 302 | .PP |
| 303 | bn_mul_recursive(\fBr\fR, \fBa\fR, \fBb\fR, \fBn2\fR, \fBdna\fR, \fBdnb\fR, \fBt\fR) operates |
| 304 | on the word arrays \fBa\fR and \fBb\fR of length \fBn2\fR+\fBdna\fR and \fBn2\fR+\fBdnb\fR |
| 305 | (\fBdna\fR and \fBdnb\fR are currently allowed to be 0 or negative) and the 2*\fBn2\fR |
| 306 | word arrays \fBr\fR and \fBt\fR. \fBn2\fR must be a power of 2. It computes |
| 307 | \&\fBa\fR*\fBb\fR and places the result in \fBr\fR. |
| 308 | .PP |
| 309 | bn_mul_part_recursive(\fBr\fR, \fBa\fR, \fBb\fR, \fBn\fR, \fBtna\fR, \fBtnb\fR, \fBtmp\fR) |
| 310 | operates on the word arrays \fBa\fR and \fBb\fR of length \fBn\fR+\fBtna\fR and |
| 311 | \&\fBn\fR+\fBtnb\fR and the 4*\fBn\fR word arrays \fBr\fR and \fBtmp\fR. |
| 312 | .PP |
| 313 | bn_mul_low_recursive(\fBr\fR, \fBa\fR, \fBb\fR, \fBn2\fR, \fBtmp\fR) operates on the |
| 314 | \&\fBn2\fR word arrays \fBr\fR and \fBtmp\fR and the \fBn2\fR/2 word arrays \fBa\fR |
| 315 | and \fBb\fR. |
| 316 | .PP |
| 317 | bn_mul_high(\fBr\fR, \fBa\fR, \fBb\fR, \fBl\fR, \fBn2\fR, \fBtmp\fR) operates on the |
| 318 | \&\fBn2\fR word arrays \fBr\fR, \fBa\fR, \fBb\fR and \fBl\fR (?) and the 3*\fBn2\fR word |
| 319 | array \fBtmp\fR. |
| 320 | .PP |
| 321 | \&\fIBN_mul()\fR calls \fIbn_mul_normal()\fR, or an optimized implementation if the |
| 322 | factors have the same size: \fIbn_mul_comba8()\fR is used if they are 8 |
| 323 | words long, \fIbn_mul_recursive()\fR if they are larger than |
| 324 | \&\fB\s-1BN_MULL_SIZE_NORMAL\s0\fR and the size is an exact multiple of the word |
| 325 | size, and \fIbn_mul_part_recursive()\fR for others that are larger than |
| 326 | \&\fB\s-1BN_MULL_SIZE_NORMAL\s0\fR. |
| 327 | .PP |
| 328 | bn_sqr_normal(\fBr\fR, \fBa\fR, \fBn\fR, \fBtmp\fR) operates on the \fBn\fR word array |
| 329 | \&\fBa\fR and the 2*\fBn\fR word arrays \fBtmp\fR and \fBr\fR. |
| 330 | .PP |
| 331 | The implementations use the following macros which, depending on the |
| 332 | architecture, may use \*(L"long long\*(R" C operations or inline assembler. |
| 333 | They are defined in \f(CW\*(C`bn_lcl.h\*(C'\fR. |
| 334 | .PP |
| 335 | mul(\fBr\fR, \fBa\fR, \fBw\fR, \fBc\fR) computes \fBw\fR*\fBa\fR+\fBc\fR and places the |
| 336 | low word of the result in \fBr\fR and the high word in \fBc\fR. |
| 337 | .PP |
| 338 | mul_add(\fBr\fR, \fBa\fR, \fBw\fR, \fBc\fR) computes \fBw\fR*\fBa\fR+\fBr\fR+\fBc\fR and |
| 339 | places the low word of the result in \fBr\fR and the high word in \fBc\fR. |
| 340 | .PP |
| 341 | sqr(\fBr0\fR, \fBr1\fR, \fBa\fR) computes \fBa\fR*\fBa\fR and places the low word |
| 342 | of the result in \fBr0\fR and the high word in \fBr1\fR. |
| 343 | .SS "Size changes" |
| 344 | .IX Subsection "Size changes" |
| 345 | \&\fIbn_expand()\fR ensures that \fBb\fR has enough space for a \fBbits\fR bit |
| 346 | number. \fIbn_wexpand()\fR ensures that \fBb\fR has enough space for an |
| 347 | \&\fBn\fR word number. If the number has to be expanded, both macros |
| 348 | call \fIbn_expand2()\fR, which allocates a new \fBd\fR array and copies the |
| 349 | data. They return \fB\s-1NULL\s0\fR on error, \fBb\fR otherwise. |
| 350 | .PP |
| 351 | The \fIbn_fix_top()\fR macro reduces \fBa\->top\fR to point to the most |
| 352 | significant non-zero word plus one when \fBa\fR has shrunk. |
| 353 | .SS "Debugging" |
| 354 | .IX Subsection "Debugging" |
| 355 | \&\fIbn_check_top()\fR verifies that \f(CW\*(C`((a)\->top >= 0 && (a)\->top |
| 356 | <= (a)\->dmax)\*(C'\fR. A violation will cause the program to abort. |
| 357 | .PP |
| 358 | \&\fIbn_print()\fR prints \fBa\fR to stderr. \fIbn_dump()\fR prints \fBn\fR words at \fBd\fR |
| 359 | (in reverse order, i.e. most significant word first) to stderr. |
| 360 | .PP |
| 361 | \&\fIbn_set_max()\fR makes \fBa\fR a static number with a \fBdmax\fR of its current size. |
| 362 | This is used by \fIbn_set_low()\fR and \fIbn_set_high()\fR to make \fBr\fR a read-only |
| 363 | \&\fB\s-1BIGNUM\s0\fR that contains the \fBn\fR low or high words of \fBa\fR. |
| 364 | .PP |
| 365 | If \fB\s-1BN_DEBUG\s0\fR is not defined, \fIbn_check_top()\fR, \fIbn_print()\fR, \fIbn_dump()\fR |
| 366 | and \fIbn_set_max()\fR are defined as empty macros. |
| 367 | .SH "SEE ALSO" |
| 368 | .IX Header "SEE ALSO" |
| 369 | \&\fIbn\fR\|(3) |